Spending and hiring are expected to suffer over uncertainties about the U.S. debt.

WASHINGTON — Despite the huge relief rally on Wall Street, the incomplete resolution of the so-called fiscal cliff will do little to boost the economy but assures an intense budget battle that is expected to weigh on spending and hiring at least over the next few months.

The New Year's Day deal let payroll taxes for all workers revert to their previous higher rate, though it avoided the worst of the "fiscal cliff" issues by blocking tax-rate increases on all but the wealthiest Americans and postponing federal spending cuts.

That means workers will start seeing on average about $20 less a week in their paychecks starting this month, a cut in incomes that is expected to dampen spending and contribute to slower hiring.

But that's not what business leaders and economists are fretting about; the payroll tax cut was meant to be temporary, and most had factored its expiration into their new year's forecast. The big concern is that the deal did nothing to reduce government spending and fell short of taking needed steps to stabilize the rising U.S. debt.

Lawmakers also left for the new Congress the hard work of raising the nation's debt limit before the end of February, the rough deadline for action in the latest Treasury Department estimates.

Policymakers still must try in the next two months to replace $1.2 trillion in automatic spending cuts over the next decade with a package that would cause less economic damage.

And the fates of many tax deductions and loopholes are up in the air because overhauls of the individual and corporate tax codes are expected to take place this year as part of a deficit-reduction plan.

Wall Street, however, rejoiced. In the exuberant first day of trading in the new year, the Dow Jones industrial average surged 308 points, or 2.4%, to nearly 13,413. The rally gave the Dow its best day since Dec. 20, 2011.

"There's relief that something got passed that was better than the worst-case scenario," said Doug Cote, chief investment strategist with ING Investment Management U.S.

But he called the rally one of "false relief" because the longer-term deficit problems remain an unresolved threat.

"There's still plenty of uncertainty, unfortunately, that remains," said John Engler, president of the Business Roundtable, a group of top corporate chief executives.

The group's quarterly survey last month projected the economy would maintain roughly last year's mediocre growth of 2% in 2013, and Tuesday's deal probably won't change that forecast much, he said.

Still, Engler said: "You can certainly say the potential for some harm was averted, but the potential for greater certainty still lies ahead."

Some analysts say prolonged uncertainty — coupled with the loss of consumer spending from higher payroll taxes — could hold back employers from hiring and spending as they wait for Congress to make more decisions about the budget.

The Bureau of Labor Statistics will release employment numbers for December on Friday, and economists are generally expecting continued steady growth of about 150,000 jobs, a decent number that would slowly bring down the unemployment rate.

But that report may be the best for months ahead if reduced demand and concerns about the upcoming budget fight cause businesses to pull back.

"The cautiousness on the part of businesses will persist," said Michael Gapen, senior U.S. economist at Barclays in New York. He reckons that the biggest hits to the labor market may be in the first quarter when companies purge payrolls after the holiday season.

The deal did extend emergency unemployment benefits for some 2 million long-term jobless workers who faced an abrupt end to their economic life support, providing about $30 billion in aid that would be pumped directly into the economy.

It also permanently fixed the alternative minimum tax, which threatened to hit millions of middle-income Americans because the provision, which was enacted in 1969 and aimed at making sure the wealthy paid some taxes, had not been indexed to inflation.

Businesses, too, expressed satisfaction with some parts of the tax agreement. Congress permanently extended much of the George W. Bush-era tax cuts, which gave companies clarity on income tax rates.

The legislation also extended the research and development tax credit until the end of 2013 and retroactively reinstated it for last year. And lawmakers extended through this year special rules that allow for accelerated depreciation. The so-called bonus depreciation allows businesses to write off 50% of the cost of capital investments made in 2013, which could help reverse the recent decline in business spending for equipment. Normally, costs are spread evenly over three to 20 years depending on the items purchased.

But corporate executives are worried about a potential default by the U.S. if the White House and Congress can't agree to lift the debt ceiling.